where the integral involves an additional variable \(d\)  as compared to the integral eq:Iac.
Proving the above identity requires the Rodrigues' formula[1]}, i.e., for \(\Re \lbrace a,b\rbrace >-1\) , one has
\(\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! (1-x)^{a}(1+x)^{b}J^{(a,b)}_{k}(x)=\frac{(-1)^k}{2^k k!}\frac{\,\mathrm {d}^k}{\,\mathrm {d}x^k}\left((1-x)^{k+a}(1+x)^{k+b}\right).\) 
